Question

find the value of x is​

Answer 1

Topic :-

Linear Equations

Given :-

$\dfrac{x+b}{a-b}=\dfrac{x-b}{a+b}$

To Find :-

Value of 'x'.

Solution :-

Cross Multiply,

( x + b )( a + b ) = ( x - b )( a - b )

Simplify it,

x( a + b ) + b( a + b ) = x( a - b ) - b( a - b )

ax + bx + ab + b² = ax - bx - ab + b²

Canceling few terms,

ax - ax + b² - b² + bx + ab = - bx - ab

0 + 0 + bx + ab = - bx - ab

bx + ab = - bx - ab

Group similar kind of terms,

bx + bx = - ab - ab

2bx = - 2ab

Divide by 2 both sides,

bx = - ab

bx + ab = 0

b( x + a ) = 0

So,

Either b = 0 or

x + a = 0 which gives

x = - a

Answer :-

So, value of x is -a.

Verification :-

$\dfrac{x+b}{a-b}=\dfrac{x-b}{a+b}$

Put x = -a in Left Hand Side ( LHS),

$\dfrac{-a+b}{a-b}=-1$

Put x = -a in Right Hand Side ( RHS),

$\dfrac{-a-b}{a+b}=-1$

We observe that LHS = RHS.

Hence, verified !